University of Isfahan Mathematics and Society 2345-6493 2 4 2018 02 20 An estimation of minimum second powers in Arch model parameters in the presence of missing data An estimation of minimum second powers in Arch model parameters in the presence of missing data 1 10 21618 10.22108/msci.2018.21618 FA Mohammadreza Salehirad Allameh Tabataba'i University Reza Habibi Journal Article 2014 10 01 Many financial and economic time series exhibit high volatility in certain periods and have relatively less clustered volatility in others, indicating cluster-wise volatility. Assuming constant variance in such cases is not reasonable. One of the modeling tools for these variations is the use of Autoregressive Conditional Heteroscedastic (ARCH) and Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. The ARCH model has various applications in econometrics and finance, including the study of volatility changes related to stock indices, gold prices, and exchange rates. One of the common methods for estimating ARCH model parameters is the Quasi-Maximum Likelihood Estimator (QMLE) method. As this estimator does not have a closed form, the estimator of the Minimum Second Powers is used for estimating ARCH model parameters, which is more efficient compared to other estimators. Missing data in time series are common, and therefore, we obtain the two-stage Minimum Second Powers estimator in the presence of missing data. This estimator has the same asymptotic efficiency as the Quasi-Maximum Likelihood Estimator. We prove its strong consistency and asymptotic normality and confirm these results through simulations. The results are applied to the data of the Tehran Stock Exchange overall index. Many financial and economic time series exhibit high volatility in certain periods and have relatively less clustered volatility in others, indicating cluster-wise volatility. Assuming constant variance in such cases is not reasonable. One of the modeling tools for these variations is the use of Autoregressive Conditional Heteroscedastic (ARCH) and Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. The ARCH model has various applications in econometrics and finance, including the study of volatility changes related to stock indices, gold prices, and exchange rates. One of the common methods for estimating ARCH model parameters is the Quasi-Maximum Likelihood Estimator (QMLE) method. As this estimator does not have a closed form, the estimator of the Minimum Second Powers is used for estimating ARCH model parameters, which is more efficient compared to other estimators. Missing data in time series are common, and therefore, we obtain the two-stage Minimum Second Powers estimator in the presence of missing data. This estimator has the same asymptotic efficiency as the Quasi-Maximum Likelihood Estimator. We prove its strong consistency and asymptotic normality and confirm these results through simulations. The results are applied to the data of the Tehran Stock Exchange overall index.

https://math-sci.ui.ac.ir/article_21618_7af2c931142898b7056e1dda5b33cf8e.pdf

University of Isfahan Mathematics and Society 2345-6493 2 4 2018 02 20 Beautiful conjectures in graph theory Beautiful conjectures in graph theory 11 30 21839 10.22108/msci.2017.21839 FA Saeid Alikhani Yazd University Somayeh Jahari Yazd University Ali Nnoroozi Tarbiat Modares University Journal Article 2016 06 30 This paper is a translation of the the following paper into Persian: [A. Bondy, Beautiful conjectures in graph theory, European Journal of Combinatorics, 37 (2014) 4–23.] This paper is a translation of the the following paper into Persian: [A. Bondy, Beautiful conjectures in graph theory, European Journal of Combinatorics, 37 (2014) 4–23.] https://math-sci.ui.ac.ir/article_21839_55f10ca92fd920593c703343b19f3fe2.pdf

University of Isfahan Mathematics and Society 2345-6493 2 4 2018 02 20 Linear algebra in middle school textbooks Linear algebra in middle school textbooks 31 50 21977 10.22108/msci.2017.21977 FA Mansoure Sabour Ferdowsi University of Mashhad Mohammad Sal Moslehian Ferdowsi University of Mashhad Journal Article 2016 12 01 In this article, we examine the content of linear algebra in newly written middle school textbooks (seventh, eighth, and ninth grades) and, while highlighting the necessities, suggest some new linear algebra content for the ninth grade level. Additionally, we point out cases that confirm the appropriateness of this proposed content. In this article, we examine the content of linear algebra in newly written middle school textbooks (seventh, eighth, and ninth grades) and, while highlighting the necessities, suggest some new linear algebra content for the ninth grade level. Additionally, we point out cases that confirm the appropriateness of this proposed content.

https://math-sci.ui.ac.ir/article_21977_633d5be082100b7bfdc2db61896ba3da.pdf

University of Isfahan Mathematics and Society 2345-6493 2 4 2018 02 20 A brief history of number theory in iran A brief history of number theory in iran 51 57 21617 10.22108/msci.2018.21617 FA Mehdi Hassani University of Zanjan Journal Article 2016 05 28 As historians consider history as a deed of decency and honor certificate of any nation, the history of mathematics certainly holds a significant position for the people of the land. Among these, the science of arithmetic has received special attention due to its distinguished position in the vast realm of mathematics. In this paper, we briefly review and examine the history of the development of arithmetic in Iran. As historians consider history as a deed of decency and honor certificate of any nation, the history of mathematics certainly holds a significant position for the people of the land. Among these, the science of arithmetic has received special attention due to its distinguished position in the vast realm of mathematics. In this paper, we briefly review and examine the history of the development of arithmetic in Iran.

https://math-sci.ui.ac.ir/article_21617_d7c0849119160be6aa3c9714a68fd661.pdf

University of Isfahan Mathematics and Society 2345-6493 2 4 2018 02 20 Fractional calculus: from theory to applications Fractional calculus: from theory to applications 59 69 22116 10.22108/msci.2017.100109.1201 FA Journal Article 2016 11 14 This article introduces fractional calculus, including the definition of fractional derivatives and integrals, as well as the governing relationships, similarities, and differences between fractional calculus and classical calculus. We also delve into the geometric interpretation of fractional derivatives and integrals. Furthermore, we present applications of fractional calculus and fractional differential equations. This article introduces fractional calculus, including the definition of fractional derivatives and integrals, as well as the governing relationships, similarities, and differences between fractional calculus and classical calculus. We also delve into the geometric interpretation of fractional derivatives and integrals. Furthermore, we present applications of fractional calculus and fractional differential equations.

https://math-sci.ui.ac.ir/article_22116_1d2a4fb6a28b2eaa6da67aecd48af4ef.pdf

University of Isfahan Mathematics and Society 2345-6493 2 4 2018 02 20 A review of entropy in mathematics: from numerical to operator forms A review of entropy in mathematics: from numerical to operator forms 71 84 22118 10.22108/msci.2017.106502.1249 FA Ali Moressaei University of Zanjan Journal Article 2017 09 17 The term entropy has acquired different meanings in various scientific disciplines, of which we refer to the most fundamental ones in this article. Here, we aim to initially provide a historical review of the concept of entropy from its numerical form to its operator form. Along the way, we will delve into some of the key theorems, inequalities, and properties of entropy. The term entropy has acquired different meanings in various scientific disciplines, of which we refer to the most fundamental ones in this article. Here, we aim to initially provide a historical review of the concept of entropy from its numerical form to its operator form. Along the way, we will delve into some of the key theorems, inequalities, and properties of entropy.

https://math-sci.ui.ac.ir/article_22118_cc325e928e0827d35432999f4712e219.pdf